ST. LOUIS -- St. Louis Blues center T.J. Oshie knew exactly what to do with the puck that completed his first three-goal game in the NHL.

That souvenir now belongs to his 10-day old daughter, Lyla Grace, who was born on March 17.

"It's definitely going to her," he said.

Oshie's hat trick and a 27-save performance by Ryan Miller led the Blues to a 5-1 rout over the Minnesota Wild on Thursday night.

St. Louis has won three in a row overall and nine straight against the Wild. The Blues lead the NHL with 107 points.

Jaden Schwartz and Brenden Morrow also scored for St. Louis, which has points in its last 10 home games. Miller improved to 9-2-1 since being acquired from Buffalo on Feb. 28.

He has a 2.03 goals against average and a .918 save percentage with the Blues.

Zach Parise scored for the Wild, who had earned points in their previous three road games but have lost six of eight overall. Darcy Kuemper made 19 saves but fell to 12-8-4. He has won just twice in nine starts.

Oshie, who has a career-high 21 goals, scored twice in the first period -- including a short-handed goal with 26 seconds left that made it 2-0.

He converted from the slot at 4:43 and then beat Kuemper on a breakaway for the Blues' fifth short-handed goal of the season.

Oshie tipped in a shot from Jay Bouwmeester at 7:18 of the third period to complete the hat trick.

"This has been an exciting couple of months for me," said Oshie, who played for the United States in the Olympics, "but she trumps everything for me."

The modest Oshie refused to take credit for his big night.

"The pucks just happened to go off my stick," he said.

But linemates David Backes and Alexander Steen were happy to heap praise on Oshie.

"He's been a horse for us all year," Backes said. "He strung a couple of great shots together and a tip on the last one.

"I couldn't be happier for him."

The Blues posted a hat trick for the second straight game as Backes scored three times in a 5-3 win at Toronto on Tuesday. That was the first time St. Louis recorded back-to-back three-goal games since Dec. 20-23, 2000, when Pavol Demitra and Michal Handzus accomplished the feat.

The Blues lead the Western Conference and are battling Boston for the Presidents' Trophy for the top mark in the NHL. They are one point ahead of the Bruins with nine games remaining for both teams.

"We wanted to make a statement to the league that we deserve to be where we're at," Oshie said. "We want that target on our backs."

St. Louis coach Ken Hitchcock believes his club is peaking at the right time.

"We're not going to be overwhelmed because we're the favorites in a playoff series," he said. "We're going to embrace it."